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Results (7 matches)

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Label Class Base field Conductor norm Rank Torsion CM Sato-Tate Regulator Period Leading coeff j-invariant Weierstrass coefficients Weierstrass equation
3872.14-b1 3872.14-b \(\Q(\sqrt{-7}) \) \( 2^{5} \cdot 11^{2} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.461921226$ 2.210217144 \( -\frac{46830231}{234256} a + \frac{212077575}{117128} \) \( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 12 a - 20\) , \( 11 a - 9\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(12a-20\right){x}+11a-9$
3872.5-b1 3872.5-b \(\Q(\sqrt{-7}) \) \( 2^{5} \cdot 11^{2} \) 0 $\Z/2\Z\oplus\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $1.461921226$ 2.210217144 \( -\frac{46830231}{234256} a + \frac{212077575}{117128} \) \( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -9 a + 23\) , \( 0\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-9a+23\right){x}$
5324.6-e1 5324.6-e \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 11^{3} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.881571669$ 2.665622171 \( -\frac{46830231}{234256} a + \frac{212077575}{117128} \) \( \bigl[1\) , \( -1\) , \( a + 1\) , \( -40 a + 50\) , \( 45 a - 83\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-40a+50\right){x}+45a-83$
5324.7-d1 5324.7-d \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 11^{3} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.881571669$ 2.665622171 \( -\frac{46830231}{234256} a + \frac{212077575}{117128} \) \( \bigl[1\) , \( -1\) , \( a\) , \( 21 a - 64\) , \( -59 a + 50\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(21a-64\right){x}-59a+50$
15488.20-d2 15488.20-d \(\Q(\sqrt{-7}) \) \( 2^{7} \cdot 11^{2} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.033734412$ 1.562859530 \( -\frac{46830231}{234256} a + \frac{212077575}{117128} \) \( \bigl[a + 1\) , \( 1\) , \( 0\) , \( -5 a + 46\) , \( 27 a + 42\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(-5a+46\right){x}+27a+42$
15488.5-d2 15488.5-d \(\Q(\sqrt{-7}) \) \( 2^{7} \cdot 11^{2} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.033734412$ 1.562859530 \( -\frac{46830231}{234256} a + \frac{212077575}{117128} \) \( \bigl[a\) , \( -a - 1\) , \( a\) , \( 33 a - 24\) , \( -7 a + 65\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(33a-24\right){x}-7a+65$
23716.5-a2 23716.5-a \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 7^{2} \cdot 11^{2} \) $2$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $0.131842497$ $1.105108572$ 3.524449760 \( -\frac{46830231}{234256} a + \frac{212077575}{117128} \) \( \bigl[1\) , \( -1\) , \( 0\) , \( -21 a - 16\) , \( -7 a - 22\bigr] \) ${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(-21a-16\right){x}-7a-22$
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  *The rank, regulator and analytic order of Ш are not known for all curves in the database; curves for which these are unknown will not appear in searches specifying one of these quantities.